Definition 8 (Perfect Elimination Ordering, Elimination Tree [1]}) 
Let \(G = (V, E)\)  be a graph and \(o = (v_1, v_2, \ldots , v_n)\)  be an ordering
of the vertices of \(G\) . Let \(N^-(G,o,i)\)  and \(N^+(G,o,i)\)  for \(i=1, \ldots , n\) 
be the set of neighbors \(v_j\)  of vertex \(v_i\)  with \(j < i\)  and \(j > i\)  respectively.
\(N^-(G,o,i) &=& \lbrace v_j |(v_i, v_j) \in E \mbox{\ and\ } j < i\rbrace \\N^+(G,o,i) &=& \lbrace v_j |(v_i, v_j) \in E \mbox{\ and\ } j > i\rbrace \) 
